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3 years ago

Find the equation of a line that is perpendicular to the line 2x-3y=9 and passes through the point (4,-1)

Mathematics

1 answer:

sashaice [31]3 years ago

6 0

Answer:

y = -3/2x + 5

Step-by-step explanation:

Step 1: find the slope

2x - 3y = 9

2x - 9 = 3y

Make y the subject of the formula by dividing both sides by 3

(2x - 9)/3 = 3y/3

( 2x - 9)/3 = y

y = 2x/3 - 9/3

y = 2x/3 - 3

m = 2x/3

Note: if two lines are perpendicular to the other, both lines are negative reciprocal of each other

m = -3/2x

Step 2 : using the point slope equation

y - y1 = m( x - x1)

( 4 , -1)

x1 = 4

y1 = -1

y -(-1) = m( x - 4)

y + 1 = -3/2( x - 4)

y + 1 = (-3x + 12)/2

y = (-3x + 12)/2 - 1

LCM = 2

y = (-3x + 12 - 2)/2

y = ( -3x + 10)/2

y = -3x/2 + 10/2

y = -3x/2 + 5

The equation of the line is

y = -3/2x + 5

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vodomira [7]

Answer:

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Step-by-step explanation:

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3 years ago

Write the mathematical expression for the following verbal expression: the product of 12 and a number is more than 190

AysviL [449]

Hello,

12(x) > 190

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3 years ago

How to find the surface area of a trapezoidal prism.

juin [17]

Answer:

(b1+b2)h+PH

Step-by-step explanation:

b1 and b2 stands for the length of the bases of the trapezoid

The h is the height of the trapezoid

The P is the perimeter of the trapezoid

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Hope this helps :)

3 0

3 years ago

Susan is on vacation at a tropical bay that has three islands. She rents a boat on Island A and plans to navigate to Island C, w

Sauron [17]

She should navigate at 45° 34' 22.7856" to go to Island C.

Given that Susan is on vacation at a tropical bay that has three islands, and she rents a boat on Island A and plans to navigate to Island C, which is 8 miles away, to determine, based on the figure below, at what angle should she navigate to go to Island C, the following calculation must be carried out, applying the cosine law:

11^2 = 8^2 + 15^2 - (2 x 8 x 15) x cos A
Cos A = (8^2 + 15^2 - 11^2) / (2x8x15)
A = arc cos (8^2 + 15^2 - 11^2) / (2x8x15)
A = arc cos (64 + 225 - 121) / 240
A = arc cos (168 / 240)
A = arc cos 0.7
A = 45.572996

Therefore, she should navigate at 45° 34' 22.7856" to go to Island C.

Learn more in brainly.com/question/24077856

5 0

2 years ago

Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=2x2i+5y2j+3z2k across the boundary of the recta

aksik [14]

Answer:

The answer is "120".

Step-by-step explanation:

Given values:

$F(x,y,z)=2x^2i+5y^2j+3z^2k \\$

differentiate the above value:

$div F =2 \frac{x^2i}{\partial x}+5 \frac{y^2j}{\partial y}+3 \frac{z^2k }{\partial z} \\$

$= 4x+10y+6z$

$\ flu \ of \ x = \int \int div F dx$

$= \int\limits^1_0 \int\limits^3_0 \int\limits^1_0 {(4x+10y+6z)} \, dx \, dy \, dz \\\\ = \int\limits^1_0 \int\limits^3_0 {(4xz+10yz+6z^2)}^{1}_{0} \, dx \, dy \\\\ = \int\limits^1_0 \int\limits^3_0 {(4x+10y+6)} \, dx \, dy \\\\ = \int\limits^1_0 {(4xy+10y^2+6y)}^3_{0} \, dx \\\\ = \int\limits^1_0 {(12x+90+18)}\, dx \\\\= {(12x^2+90x+18x)}^{1}_{0} \\\\= {(12+90+18)} \\\\=30+90\\\\= 120$

6 0

3 years ago